# Problem of the Week

## Updated at Sep 16, 2019 4:41 PM

For this week we've brought you this equation problem.

How would you solve $$\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}$$?

Here are the steps:

$\frac{u}{4\times 5}\times \frac{u-3}{5}=-\frac{1}{50}$

 1 Simplify  $$4\times 5$$  to  $$20$$.$\frac{u}{20}\times \frac{u-3}{5}=-\frac{1}{50}$2 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$\frac{u(u-3)}{20\times 5}=-\frac{1}{50}$3 Simplify  $$20\times 5$$  to  $$100$$.$\frac{u(u-3)}{100}=-\frac{1}{50}$4 Multiply both sides by $$100$$.$u(u-3)=-2$5 Expand.${u}^{2}-3u=-2$6 Move all terms to one side.${u}^{2}-3u+2=0$7 Factor $${u}^{2}-3u+2$$.1 Ask: Which two numbers add up to $$-3$$ and multiply to $$2$$?$$-2$$ and $$-1$$2 Rewrite the expression using the above.$(u-2)(u-1)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(u-2)(u-1)=0$8 Solve for $$u$$.1 Ask: When will $$(u-2)(u-1)$$ equal zero?When $$u-2=0$$ or $$u-1=0$$2 Solve each of the 2 equations above.$u=2,1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=2,1$Doneu=2,1